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Extensive research into high temperature superconducting cuprates is nowfocused upon identifying the relationship between the classic 'pseudogap'phenomenon$^{1,2}$ and the more recently investigated density wavestate$^{3-13}$. This state always exhibits wave vector $Q$ parallel to theplanar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry formfactor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become akey objective$^{18-30}$ of this field. To accomplish this, one must identifythe momentum-space ($k$-space) states contributing to the dFF-DW spectralweight, determine their particle-hole phase relationship about the Fermienergy, establish whether they exhibit a characteristic energy gap, andunderstand the evolution of all these phenomena throughout the phase diagram.Here we use energy-resolved sublattice visualization$^{14}$ of electronicstructure and show that the characteristic energy of the dFF-DW modulations isactually the 'pseudogap' energy $\Delta_{1}$. Moreover, we demonstrate that thedFF-DW modulations at $E=-\Delta_{1}$ (filled states) occur with relative phase$\pi$ compared to those at $E=\Delta_{1}$ (empty states). Finally, we show thatthe dFF-DW $Q$ corresponds directly to scattering between the 'hot frontier'regions of $k$-space beyond which Bogoliubov quasiparticles cease toexist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistentwith particle-hole interactions focused at the pseudogap energy scale andbetween the four pairs of 'hot frontier' regions in $k$-space where thepseudogap opens.

Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State